Light with energy flux 36w/cm2 is incident on a well polished metal square plate of side 2cm. The force experienced by it is

Options

A. `0.96 muN`
B. `0.24 muN`
C. `0.12 mu N`
D. `0.36 muN`

Answer

To solve the problem of calculating the force experienced by a polished metal square plate when light is incident on it, we will follow these steps:

### Step 1: Understand the Given Information
- Energy flux (I) = 36 W/cm²
- Side of the square plate = 2 cm

### Step 2: Convert Units
1. Convert the energy flux from W/cm² to W/m²:
\[ I = 36 \, \text{W/cm}^2 = 36 \times 10^4 \, \text{W/m}^2 \]

2. Convert the side length of the square plate from cm to meters:
\[ \text{Side length} = 2 \, \text{cm} = 2 \times 10^{-2} \, \text{m} \]

### Step 3: Calculate the Area of the Square Plate
The area (A) of the square plate can be calculated using the formula for the area of a square:
\[ A = \text{side}^2 = (2 \times 10^{-2} \, \text{m})^2 = 4 \times 10^{-4} \, \text{m}^2 \]

### Step 4: Use the Formula for Force
The force (F) experienced by the plate due to the incident light can be calculated using the formula:
\[ F = \frac{2 \cdot I \cdot A}{c} \]
where \(c\) is the speed of light in vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step 5: Substitute the Values into the Formula
Substituting the values we have:
\[ F = \frac{2 \cdot (36 \times 10^4 \, \text{W/m}^2) \cdot (4 \times 10^{-4} \, \text{m}^2)}{3 \times 10^8 \, \text{m/s}} \]

### Step 6: Simplify the Expression
1. Calculate the numerator:
\[ 2 \cdot 36 \cdot 4 = 288 \]
Thus, the numerator becomes:
\[ 288 \times 10^4 \]

2. Now, substitute back into the force equation:
\[ F = \frac{288 \times 10^4}{3 \times 10^8} \]

3. Simplifying further:
\[ F = \frac{288}{3} \times 10^{-4} = 96 \times 10^{-4} \, \text{N} \]

### Step 7: Convert to Micro Newtons
To express the force in micro Newtons:
\[ F = 96 \times 10^{-4} \, \text{N} = 0.96 \, \mu\text{N} \]

### Final Answer
The force experienced by the plate is:
\[ F = 0.96 \, \mu\text{N} \]

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